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Mirrors > Home > MPE Home > Th. List > clelsb3 | Structured version Visualization version Unicode version |
Description: Substitution applied to an atomic wff (class version of elsb3 2434). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
clelsb3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . 3 | |
2 | 1 | sbco2 2415 | . 2 |
3 | nfv 1843 | . . . 4 | |
4 | eleq1 2689 | . . . 4 | |
5 | 3, 4 | sbie 2408 | . . 3 |
6 | 5 | sbbii 1887 | . 2 |
7 | nfv 1843 | . . 3 | |
8 | eleq1 2689 | . . 3 | |
9 | 7, 8 | sbie 2408 | . 2 |
10 | 2, 6, 9 | 3bitr3i 290 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wsb 1880 wcel 1990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-cleq 2615 df-clel 2618 |
This theorem is referenced by: hblem 2731 cbvreu 3169 sbcel1v 3495 rmo3 3528 kmlem15 8986 iuninc 29379 measiuns 30280 ballotlemodife 30559 bj-nfcf 32920 sbcel1gvOLD 39094 ellimcabssub0 39849 |
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